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A Robust Test for Checking the Homogeneity of Variability Measures and Its Application to the Analysis of Implicit Attitudes

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  • Ryan C. Erps
  • Kimihiro Noguchi

    (Western Washington University)

Abstract

A new two-sample test for comparing variability measures is proposed. To make the test robust and powerful, a new modified structural zero removal method is applied to the Brown–Forsythe transformation. The t -test-based statistic allows results to be expressed as the ratio of mean absolute deviations from median. Extensive simulation study demonstrates that the proposed test is robust to small or unequal sample sizes across many distributions. Moreover, careful exploratory analysis provides a new method for calculating the implicit association test scores for reaction time data with multiplicative treatment effects. Using this, a possible difference between variability of men and women’s implicit attitudes toward gay men is analyzed.

Suggested Citation

  • Ryan C. Erps & Kimihiro Noguchi, 2020. "A Robust Test for Checking the Homogeneity of Variability Measures and Its Application to the Analysis of Implicit Attitudes," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 403-425, August.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:4:p:403-425
    DOI: 10.3102/1076998619883874
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    References listed on IDEAS

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    1. Kimihiro Noguchi & Fernando Marmolejo-Ramos, 2016. "Assessing Equality of Means Using the Overlap of Range-Preserving Confidence Intervals," The American Statistician, Taylor & Francis Journals, vol. 70(4), pages 325-334, October.
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    6. W. G. S. Hines & R. J. O'Hara Hines, 2000. "Increased Power with Modified Forms of the Levene (Med) Test for Heterogeneity of Variance," Biometrics, The International Biometric Society, vol. 56(2), pages 451-454, June.
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    8. Kimihiro Noguchi & Yulia Gel, 2010. "Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 897-913.
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